Preheat oven to 350°F. Line two baking sheets with parchment paper.
Make crumb: Combine flour, brown sugar, granulated sugar, cinnamon, and salt. Stir in melted butter until clumpy. Chill.
Whisk dough dry ingredients: flour, baking powder, baking soda, salt, pumpkin pie spice, and cinnamon.
Cream softened butter with brown sugar and granulated sugar until light and fluffy.
Beat in vanilla, then mix in pumpkin puree until smooth and fully combined.
Add dry mix to wet and stir just until no dry spots remain. Let dough rest 5 minutes.
Scoop about 2 tablespoons dough per cookie onto sheets, spacing 2 inches apart.
Indent each mound slightly with a spoon. Pile on crumb, pressing lightly so it sticks.
Bake one sheet at a time for 12–14 minutes, until edges are set and crumbs look golden.
Cool cookies on the pan 10 minutes, then move to a rack to finish cooling.
Whisk powdered sugar, milk, vanilla, and a pinch of cinnamon until pourable.
Drizzle glaze over cooled cookies. Let set before serving or storing.